STUDY ON MECHANICAL AND THERMODYNAMIC PROPERTY OF MOLECULAR CRYOCRYSTALS CO2 AND n2o UNDER PRESSURE

STUDY ON MECHANICAL AND THERMODYNAMICUNDER PRESSURE NGUYEN QUANG HOC, HOANG VAN TICH Hanoi National University of Education,Xuan Thuy, Cau Giay, Hanoi NGUYEN DUC HIEN Tay Nguyen Universi

STUDY ON MECHANICAL AND THERMODYNAMIC

UNDER PRESSURE

NGUYEN QUANG HOC, HOANG VAN TICH Hanoi National University of Education,Xuan Thuy, Cau Giay, Hanoi

NGUYEN DUC HIEN Tay Nguyen University, 457 Le Duan, Buon Me Thuot City

Abstract The mechanical and thermodynamic properties (such as the nearest neighbor distance ,the molar volume, the adiabatic and isothermal compressibilities, the thermal expansion coef-ficient, the specific heats at constant volume and at constant pressure) of some cryocrystals of many atoms with face-centered cubic structure such as α-CO 2 , α-N 2 O, at various temperatures and pressures up to 10 GPa are investigated by the statistical moment method (SMM) in statistical mechanics and compared with the experimental data.

I INTRODUCTION Molecular crystals are characterized by strong intramolecular forces and much weaker intermolecular forces Therefore, a molecule in the crystal retains its identity to a great extent Nevertheless, these solids represent the next progression in complexity from the monoatomic inert gas solids.

High-pressure spectroscopic studies provide useful data for refining the various model potentials which are used for prediction of the physical properties of such systems as well

as for the formation of various crystalline phases [1] These studies on molecular crystals also offer quite interesting aspects concerning the shape and nature of different types of forces In high-pressure data provide a stringent test of various potentials which have been derived and tested mainly on the basis of temperature dependent properties of these solids

at ambient pressure.

system Its high-pressure behavior is therefore of fundamental importance in planetary

crystalline structure of such solids is mainly determined by weak intermolecular interac-tions, while the molecule itself is held together by strong intramolecular forces From the

the hybridization properties of the carbon atom, which are strongly affected by the high pressure conditions [2].

sys-tematically investigated by using first-principle lattice dynamics calculation Geometri-cally, likely transition pathways are derived from the dynamical instability of the molecular crystals under high pressures [3]

According to [4, 14], the phase diagram of CO2 composes 5 phases CO2-I (phase I

performed a series of first principles calculations, including full structural optimizations, phonon spectra and free energies in order to study the stability and properties of the phases proposed experimentally up to 50 GPa and 1500 K The DFT calculations were carried out within the Perdew-Burke-Ernzerhof [6] generalized gradient approximation (CGA) using the ABINIT code [7] which implements plane-wave basis sets[8]

(MGK) electron-gas model[9] that worked well in calculating the structure and properties

of molecular crystals [10]

A combination of ab initio molecular dynamic simulations and fully relaxed total

A constant pressure Monte Carlo formalism, lattice dynamics and classical perturbation theory are used to calculate the thermal expansion, pressure-volume relation at room tem-perature, the temperature dependence of zone center libron frequencies and the pressure

and at and 300K have been calculated using energy optimization, Monte Carlo methods

in an ensemble with periodic, deformable boundary conditions and lattice dynamics [13].

or-dered cubic form, space group Pa3, up to 4.8 GPa where transition to a new solid occurs.

influ-ence of quantum effects on condensed matter Up to now , there has been considerable interest in structural and thermodynamic properties of these crystals under temperature and pressure In line with this general interest and encouraged by the essential success of our calculations, as applied to other substances [1], we tried to consider the mechanical and thermodynamic properties (such as the nearest neighbor distance, the molar volume , the adiabatic and isothermal compressibilities, the thermal expansion coefficient, the specific heats at constant volume and at constant pressure) of some cryocrystals of many

and pressures up to 10 GPa are investigated by the statistical moment method (SMM) in statistical mechanics and compared with the experimental data Specifics heat at constant volume for these crystals are studied by combining the SMM and the self- consistent field method taking account of lattice vibrations and molecular rotational motion [16].

It is known that the interaction potential between two atoms in α phase of

the form of the Lennard-Jones pair potential

φ(r) = 4ε



r

r

(1) where σ is the distance in which φ(r) = 0 and ε is the depth of potential well The values of

the coordinate sphere method and the results in [17], we obtain the values of parameters

a

265.298

a

− 64.01

 ,

a

4410.797

a

− 346.172

 ,

a

803.555

a

− 40.547



a

a

− 305.625

 ,

where a is the nearest neighbor distance at temperature T At temperature 0K, the

thermal expansion coefficient β and the specific heats at constant volume and constant

shown in [17] In general, our calculations are in qualitative agreement with experiments.

In order to determine the thermodynamic quantities at various pressures, we must find the nearest neighbor distances The equation for calculating the nearest neighbor distances at pressure P and at temperature T has the form [17]





3

3

(3)

equation and therefore, it only has approximate solution From that, the equation for calculating the nearest neighbor distances at pressure P and at temperature 0K has the form

3

3

After finding the solution a(p,0K) from (4), we can calculate a (p,T ) and other thermo-dynamic quantities This means is applied to crystal at low pressures For crystal at high pressures, we must directly find the solution from (4).

The solution of this equation is y = 1.281967, i.e the nearest neighbor distance under the condition p = 0.5 kbar, T = 0K takes a value m At temperature 0K and pressure p,

pressure range of 0 to 4.8 GPa and in the temperature range of 0 to 130 K Our numerical results are carried out in these ranges of temperature and pressure We only have the

results will be more consistent with experiments by taking account of molecular rotation and intermolecular motion.

4.10

4.15

4.20

4.25

4.30

T, K

p = 0

p = 0.5 kbar

p = 1 kbar

2

1

4 1 0

4 1 5

4 2 0

4 2 5

4 3 0

T , K

P = 0

P = 0 5 k b a r

P = 1 k b a r

F i g u r e 2 G r a p h s f o r α - N 2O a t p = 0 , p = 0 5 k b a r a n d p = 1 k b a r

2 0 4 0 6 0 8 0 1 0 0 1 2 0

f o r α - C O 2 a t p = 0 , p = 0 5 k b a r a n d p = 1 k b a r

 T

 S

T , K

χs p = 1 k b a r

χT p = 1 k b a r

χS p = 0 5 k b a r

χΤ p = 0 5 k b a r

χs p = 0

χT p = 0

 T

 S

χs p = 1 k b a r

χT p = 1 k b a r

χS p = 0 5 k b a r

χΤ p = 0 5 k b a r

χs p = 0

χT p = 0

T , K

f o r α - N 2O a t p = 0 , p = 0 5 k b a r a n d p = 1 k b a r

F i g u r e . G r a p h s  T  f o r - C O 2 a t p = 0 , p = 0 5 k b a r a n d p = 1 k b a r

-4 K

T , K

p = 0

p = 0 , 5 k b a r

p = 1 k b a r

p = 0

p = 0 5 k b a r

p = 1 k b a r

T , K

F i g u r e . G r a p h s  T f o r α - N 2O a t p = 0 , p = 0 5 k b a r a n d p = 1 k b a r

1 0

2 0

F i g u r e . G r a p h s C V(T ) , Cp(T ) f o r α- C O 2 a t p = 0 , p = 0 5 k b a r a n d p = 1 k b a r

C V

T , K

C V ( p = 0 )

C P ( p = 0 )

C V ( p = 0 , 5 k b a r )

C P ( p = 0 , 5 k b a r )

C V ( p = 1 k b a r )

C P ( p = 1 k b a r )

1 0

1 5

2 0

2 5

F i g u r e . G r a p h s C V(T ) , C p(T ) f o r α- N 2O a t p = 0 , p = 0 5 k b a r a n d p = 1 k b a r

C V ( p = 0 )

C P ( p = 0 )

C V ( p = 0 , 5 k b a r )

C

P ( p = 0 , 5 k b a r )

C

V ( p = 1 k b a r )

C P ( p = 1 k b a r )

C V

T , K

3 6

3 7

3 8

3 9

T , K

6 G P a

1 0 G P a

F i g u r e 9 G r a p h s a ( T ) f o r α- C O 2 a t p = 2 G P a , p = 6 G P a a n d p = 1 0 G P a

3 8

3 9

4 0

T , K

1 G P a

4 G P a

F i g u r e 1 0 G r a p h s a ( T ) f o r α- N 2O a t p = 1 G P a , p = 2 G P a a n d p = 4 G P a

0 0

0 2

0 4

E X P T [ , ]

S M M

19 20

ACKNOWLEDGMENT This paper is carried out with the financial support of the HNUE project under the code SPHN-10-472.

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Received 30-09-2011.